Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
A) x + y = 24
B) x^2 + y^2 = 306
A) x = 24 -y
Then substituting this into B)
(24 - y)^2 +y^2 = 306
576 -48y +y^2 + y^2 = 306
2 y^2 -48y + 270 = 0
x1 = 15
x2 = 9
Answer:
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Step-by-step explanation:
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It's a rectangle so it will be formed on the coordinate which is 3units above dot(3,5) in picture where above the dot there is no point .
Answer:
Step-by-step explanation:
Given
Quadrant III
Required
Determine
We have:
We know that:
This gives:
Collect like terms
Take LCM and solve
Take the square roots of both sides
Sin is negative in quadrant III. So:
Calculate
We have:
So:
Rationalize
So, we have:
Substitute:
Take LCM
Answer:
the triangle PQR is similar to RTS
Step-by-step explanation:
QR : RT
2 : 6
this 1:3 ratio is also seen in PR (4) with RS (12)